課程名稱︰普通物理學甲上
課程性質︰必帶
課程教師︰陳智泓
開課學院：理學院
開課系所︰化學系
考試日期（年月日）︰102/12/5
考試時限（分鐘）：110分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
普通物理學期中考
Exam hours: 10:20am ~ 12:10pm on 12/5/2013
→ 2 ︿
1. (10%)A force F =(cx-3x ) i acts on a particle as the particle moves along an
→
axis, with F in newtons, x in meters, and c a constant. At x=0m, the
particle's kinetic energy is 19J; at x=4m, it is 11J. Find c.
2
2. An object of mass m is acted on by a conervative force given by F =-Ax-Bx ,
with F in newtons, x in meters, and A and B positive constants. Take the
potential energy associated with the force to be zero when the object is at
x=0.
(a) (10%) Find an expression for the potential energy as a function of x.
(b) (10%) What would be the answer if the potential energy of the system
is taken to be -C when the object is at x=0?
(c) (10%) If the particle has speed v at some point a distance d to the
right of the origin, what speed will it have when it reaches the
origin?
3. (10%) In the Fig. (1), block 2 (with mass m ) is at rest on a fritionless
2
surface and touching the end of an unstretched spring of spring constant k.
The other end of the spring is fixed to a wall. Block 1 (with mass m ),
1
traveling at speed v , collides with block 2, and the two blocks stick
1
together. When the blocks momentarily stop, by what distance is the spring
compressed? State your answer in terms of the given variables.
第三題的圖 Fig. 1: http://ppt.cc/9Ovs
4. The Fig. (2) shows a baseball of mass m just before and just after it
→
collides with a bat. Just before, the ball has velocity v and angle θ .
1 1
→
Just after, it is traveling directly upward with velocity v . The duration
2
of the collisioin is Δt. What are the
(a) (5%) magnitude and
(b) (5%) direction (relative to the positive directioin of the x axis) of
the impulse on the ball from the bat?
第四題的圖 Fig. 2: http://ppt.cc/q-sU
5. In the Fig. (3), a wheel of radius R is mounted on a frictionless
horizontal axis. The rotational inertia of the wheel about the axis is I.
A massless cord wrapped around the wheel's circumference is attached to a
box of mass m. The system is released from rest. When the box has a kinetic
energy of K, what are
(a) (10%) the wheel's rotational kinetic energy and
(b) (10%) the distance the box has fallen? Assume free-call acceleration
to be equal to g.
第五題的圖 Fig. 3: http://ppt.cc/KlR2
6. (10%) In the Fig. (4), a small block of mass m slides down a frictionless
surface through height h and then sticks to a uniform vertical rod of
mass M and length d. The rod pivots about point O through angle θ before
momentarily stopping. Find θ.
第六題的圖 Fig. 4: http://ppt.cc/u~Hj
7. (10%) A cockroach of mass m lies on the rim of a uniform disk of mass 3m
that can rotate freely about its center like a merry-go-round. Initially
the cockroach and disk rotate together with an angular velocity ω .
0
Then the cockroach walks halfway to the center of the disk. What then is
the angular velocity of the cockroach-disk system?
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